Constraint Optimization by Linear Approximation

Constraint Optimization by Linear Approximation

Constraint Optimization by Linear Approximation

I am trying to solve an optimization problem where I need to choose 150 variables to maximize an objective function subject to some non-linear constraints. In my program there is one main constraint and all the other ones just require that the choice variables be strictly positive.

Is there a way to take care of the strictly positive constraints without having to add 150 constraints to the code (some kind of a common requirement to keep the choice variables greater or equal to, say 10^-6)?